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From desruisse...@apache.org
Subject svn commit: r1690289 - in /sis/branches/JDK8/core/sis-referencing/src: main/java/org/apache/sis/referencing/operation/projection/ test/java/org/apache/sis/referencing/operation/projection/
Date Fri, 10 Jul 2015 17:20:09 GMT
Author: desruisseaux
Date: Fri Jul 10 17:20:09 2015
New Revision: 1690289

URL: http://svn.apache.org/r1690289
Log:
Analyzed the impact of using the series expansion given by §1.3.3 in Geomatics Guidance Note
number 7 part 2 (April 2015)
instead of the current iterative method. Our benchmarks show that the series expansion is
twice faster than the iterative
method for an excentricity relatively small like the Earth's one, but its precision decrease
as the excentricity increase.
Numbers are in the MercatorAlternative test class.

Added:
    sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/MercatorAlternative.java
  (with props)
Modified:
    sis/branches/JDK8/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/LambertConformal.java
    sis/branches/JDK8/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/NormalizedProjection.java
    sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/NormalizedProjectionTest.java

Modified: sis/branches/JDK8/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/LambertConformal.java
URL: http://svn.apache.org/viewvc/sis/branches/JDK8/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/LambertConformal.java?rev=1690289&r1=1690288&r2=1690289&view=diff
==============================================================================
--- sis/branches/JDK8/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/LambertConformal.java
[UTF-8] (original)
+++ sis/branches/JDK8/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/LambertConformal.java
[UTF-8] Fri Jul 10 17:20:09 2015
@@ -46,7 +46,7 @@ import static java.lang.Double.*;
 
 
 /**
- * <cite>Lambert Conical Conformal</cite> projection (EPSG codes 9801, 9802,
9803).
+ * <cite>Lambert Conical Conformal</cite> projection (EPSG codes 9801, 9802,
9803, 9826, 1051).
  * See the <a href="http://mathworld.wolfram.com/LambertConformalConicProjection.html">Lambert
conformal
  * conic projection on MathWorld</a> for an overview.
  *

Modified: sis/branches/JDK8/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/NormalizedProjection.java
URL: http://svn.apache.org/viewvc/sis/branches/JDK8/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/NormalizedProjection.java?rev=1690289&r1=1690288&r2=1690289&view=diff
==============================================================================
--- sis/branches/JDK8/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/NormalizedProjection.java
[UTF-8] (original)
+++ sis/branches/JDK8/core/sis-referencing/src/main/java/org/apache/sis/referencing/operation/projection/NormalizedProjection.java
[UTF-8] Fri Jul 10 17:20:09 2015
@@ -936,6 +936,11 @@ public abstract class NormalizedProjecti
      *   <li>φ(∞)   =  -π/2.</li>
      * </ul>
      *
+     * <b>Note:</b> §1.3.3 in Geomatics Guidance Note number 7 part 2 (April
2015) uses a series expansion instead.
+     * The series expansion is twice faster than the iterative method used here for the same
precision, but this
+     * precision is achieved "only" for relatively small excentricity like the Earth's one.
+     * See the {@code MercatorAlternative} class in the test package for more discussion.
+     *
      * @param  expOfSouthing The <em>reciprocal</em> of the value returned by
{@link #expOfNorthing}.
      * @return The latitude in radians.
      * @throws ProjectionException if the iteration does not converge.

Added: sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/MercatorAlternative.java
URL: http://svn.apache.org/viewvc/sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/MercatorAlternative.java?rev=1690289&view=auto
==============================================================================
--- sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/MercatorAlternative.java
(added)
+++ sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/MercatorAlternative.java
[UTF-8] Fri Jul 10 17:20:09 2015
@@ -0,0 +1,144 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.sis.referencing.operation.projection;
+
+import java.util.Random;
+import java.io.IOException;
+import java.io.PrintStream;
+import org.apache.sis.math.Statistics;
+import org.apache.sis.math.StatisticsFormat;
+import org.apache.sis.measure.Latitude;
+
+import static java.lang.Math.*;
+
+
+/**
+ * Implements the series expansion given by §1.3.3 in Geomatics Guidance Note number 7 part
2 – April 2015.
+ * This series expansions computes the latitude φ from {@code exp(-northing)} (ignoring
non-relevant terms
+ * for this discussion). It is implemented in the {@link NormalizedProjection#φ(double)}
method by an
+ * iterative process.
+ *
+ * <p>In our measurement, both the iterative process used in SIS and the series expansions
given by EPSG
+ * have the same accuracy when applied on the WGS84 ellipsoid. However the EPSG formula is
2 times faster.
+ * On the other hand, accuracy of the EPSG formula decreases when we increase the excentricity,
+ * while the iterative process keeps its accuracy (at the cost of more iterations).
+ * For the Earth (excentricity of about 0.082) the errors are less than 0.01 millimetres.
+ * But the errors become centimetric (for a planet of the size of the Earth) before excentricity
0.2
+ * and increase quickly after excentricity 0.3.</p>
+ *
+ * @author  Martin Desruisseaux (Geomatys)
+ * @since   0.6
+ * @version 0.6
+ * @module
+ */
+public final class MercatorAlternative {   // No 'strictfp' keyword here since we want to
compare with Mercator class.
+    /**
+     * Coefficients used in the series expansion.
+     */
+    private final double c2χ, c4χ, c6χ, c8χ;
+
+    /**
+     * Creates a new instance for the excentricty of the WGS84 ellipsoid, which is approximatively
0.08181919084262157.
+     * Reminder: the excentricity of a sphere is 0.
+     */
+    public MercatorAlternative() {
+        this(0.00669437999014133);  // Squared excentricity.
+    }
+
+    /**
+     * Creates a new instance for the given squared excentricity.
+     *
+     * @param e2 the square of the excentricity.
+     */
+    public MercatorAlternative(final double e2) {
+        final double e4 = e2 * e2;
+        final double e6 = e2 * e4;
+        final double e8 = e4 * e4;
+        /*
+         * For each line below, add the smallest values first in order to reduce rounding
errors.
+         * The smallest values are the one using the excentricity raised to the highest power.
+         */
+        c2χ  =    13/   360.* e8  +   1/ 12.* e6  +  5/24.* e4  +  e2/2;
+        c4χ  =   811/ 11520.* e8  +  29/240.* e6  +  7/48.* e4;
+        c6χ  =    81/  1120.* e8  +   7/120.* e6;
+        c8χ  =  4279/161280.* e8;
+    }
+
+    /**
+     * Alternative of {@link NormalizedProjection#φ(double)}.
+     *
+     * @param  t The {@code expOfSouthing} parameter value.
+     * @return The latitude (in radians) for the given parameter.
+     */
+    final double φ(final double t) {
+        final double χ = PI/2 - 2*atan(t);
+        return c8χ * sin(8*χ) +   // Add the smallest values first for reducing rounding
errors.
+               c6χ * sin(6*χ) +
+               c4χ * sin(4*χ) +
+               c2χ * sin(2*χ) + χ;
+    }
+
+    /**
+     * Performs a comparison between φ values computed by the iterative method (the current
SIS method)
+     * and φ values computed by series expansion (this alternative). The result is printed
to the standard
+     * output stream.
+     *
+     * @param  projection The projection to compare to.
+     * @param  numSamples Number of random sample values.
+     * @throws ProjectionException if an error occurred in {@link NormalizedProjection#φ(double)}.
+     */
+    public static void compare(final NormalizedProjection projection, final int numSamples)
throws ProjectionException {
+        final MercatorAlternative alt = new MercatorAlternative(projection.excentricitySquared);
+        final Statistics iterativeMethodErrors = new Statistics("Iterative method error");
+        final Statistics seriesExpansionErrors = new Statistics("Series expansion error");
+        final Statistics methodDifferences     = new Statistics("Δ (iterative - series)");
+        final Random random = new Random();
+        for (int i=0; i<numSamples; i++) {
+            final double φ_deg = random.nextDouble() * (Latitude.MAX_VALUE - Latitude.MIN_VALUE)
+ Latitude.MIN_VALUE;
+            final double φ     = toRadians(φ_deg);
+            final double t     = 1 / projection.expOfNorthing(φ, projection.excentricity
* sin(φ));
+            final double byIterativeMethod = toDegrees(projection.φ(t));
+            final double bySeriesExpansion = toDegrees(alt.φ(t));
+
+            iterativeMethodErrors.accept(abs(φ_deg - byIterativeMethod));
+            seriesExpansionErrors.accept(abs(φ_deg - bySeriesExpansion));
+            methodDifferences.accept(byIterativeMethod - bySeriesExpansion);
+        }
+        final PrintStream out = System.out;
+        out.println("Comparison of two different way to compute φ for excentricity " + projection.excentricity);
+        out.println("Values are in degrees, ");
+        final StatisticsFormat format = StatisticsFormat.getInstance();
+        format.setBorderWidth(1);
+        try {
+            format.format(new Statistics[] {iterativeMethodErrors, seriesExpansionErrors,
methodDifferences}, out);
+        } catch (IOException e) {
+            throw new AssertionError(e);
+        }
+        out.flush();
+    }
+
+    /**
+     * Executes {@link #compare(NormalizedProjection, int)} for the excentricity of the WGS84
ellipsoid.
+     * The result is printed to the standard output stream.
+     *
+     * @param  args ignored.
+     * @throws ProjectionException if an error occurred in {@link NormalizedProjection#φ(double)}.
+     */
+    public static void main(String[] args) throws ProjectionException {
+        compare(new NoOp(true), 2000000);
+    }
+}

Propchange: sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/MercatorAlternative.java
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    svn:eol-style = native

Propchange: sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/MercatorAlternative.java
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    svn:mime-type = text/plain;charset=UTF-8

Modified: sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/NormalizedProjectionTest.java
URL: http://svn.apache.org/viewvc/sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/NormalizedProjectionTest.java?rev=1690289&r1=1690288&r2=1690289&view=diff
==============================================================================
--- sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/NormalizedProjectionTest.java
[UTF-8] (original)
+++ sis/branches/JDK8/core/sis-referencing/src/test/java/org/apache/sis/referencing/operation/projection/NormalizedProjectionTest.java
[UTF-8] Fri Jul 10 17:20:09 2015
@@ -16,6 +16,7 @@
  */
 package org.apache.sis.referencing.operation.projection;
 
+import java.util.Random;
 import org.opengis.referencing.operation.TransformException;
 import org.opengis.test.referencing.TransformTestCase;
 import org.apache.sis.referencing.operation.transform.AbstractMathTransform1D;
@@ -266,6 +267,30 @@ public final strictfp class NormalizedPr
         }
     }
 
+    /**
+     * Performs a comparison between φ values computed by the iterative method (the current
SIS method)
+     * and φ values computed by series expansion (this alternative).
+     * See {@link MercatorAlternative} for a discussion.
+     *
+     * @throws ProjectionException if an error occurred in {@link NormalizedProjection#φ(double)}.
+     *
+     * @see MercatorAlternative
+     */
+    @Test
+    public void compareWithSeriesExpansion() throws ProjectionException {
+        final NormalizedProjection projection = new NoOp(true);
+        final MercatorAlternative alternative = new MercatorAlternative(projection.excentricitySquared);
+        final Random random = TestUtilities.createRandomNumberGenerator();
+        final int numSamples = 2000;
+        for (int i=0; i<numSamples; i++) {
+            final double φ = random.nextDouble() * PI - PI/2;
+            final double t = 1 / projection.expOfNorthing(φ, projection.excentricity * sin(φ));
+            final double byIterativeMethod =  projection.φ(t);
+            final double bySeriesExpansion = alternative.φ(t);
+            assertEquals(bySeriesExpansion, byIterativeMethod, 1E-11);
+        }
+    }
+
     /**
      * Tests the {@link NormalizedProjection#dy_dφ(double, double)} method.
      *



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